Analytical Mesoscale Modeling of Aeolian Sand Transport

Transcription

1 Analytical Mesoscale Modeling of Aeolian Sand Transport Marc Lämmel, Anne Meiwald, Klaus Kroy GeoFlo16 Dresden

2 Aeolian Sand Transport

3 Mesoscale Process potentially amenable to analytical modeling

4 Mean-Field approach A. Valance & BBC

5 Two-species approach saltation A. Valance & BBC reptation

6 Aeolian Structure Formation s q x q 1 2 q q s

7 Mesoscale Phenomena saltation z h l x megaripple dust

8 HEIGHT RESOLVED particle concentration particle velocity particle flux hop length & height wind speed J. Fluid Mech. (1964), vol. 20, part 2, pp Printed in Great Britain Saltation of uniform grains in air By P. R. OWEN Department of Aeronautics, Imperial College, London 225 DISTRIBUTIONS of grain trajectories (Received 14 April 1964) The interaction between a turbulent wind and the motion of uniform saltating

9 Analytically Feasible Tasks Hierarchical Approach z h Single Trajectory Distribution of Trajectories x 2 Species J. Fluid Mech. (2004), vol. 510, pp c 2004 Cambridge University Press DOI: /S Printed in the United Kingdom Compare to Experiments & Simulation Atwo-speciesmodelofaeoliansandtransport By B R U N O A N D R E O T T I 4 New Journal of Physics T h e o p e n a c c e s s j o u r n a l f o r p h y s i c s A two-species continuum model for aeolian sand transport MLämmel, D Rings and K Kroy 1 Institute for Theoretical Physics University of Leipzig, Postfach ,

10 particle distribution P (z,h) Prob to observe particle on trajectory of height h at z z h x

11 particle distribution P h(z,h) =P (z h)p h(h) wind 2-spec Prob for particle at z if on this trajectory z h Prob for trajectory of height h x

12 P h(h) / =? e h/ h Reptation/Splash J. Fluid Mech. (1983), vol. 130, pp Printed in Great Britain ~ barometer formula with A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles granular temperature By J. T. JENKINS Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, New York AND s. B. SAVAGE Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Quebec 187 Saltation h / N ; P (survival) / e N

13 particle distribution P h(z,h) =P (z h)p h(h) Prob for particle on z this trajectory at z e h/ h h h x

14 particle distribution P h(z,h) =P (z h)p h(h) z 1 2h 1 p e h/ h 1 z/h h h x

15 particle distribution P h(z,h) =P (z h)p h(h) h p 1 1 z/h e h/ h h z/h h/ h

16 height-resolved observables grain density horizontal flux vertical flux grain-borne stress hop length distribution hop length distribution (z) j(z) (z) g (z) P (z,l) P (`) `(0)

17 particle distribution Z h(z) = dhp h(z,h) Prob for particle at z for any trajectory ln(4 h/z) 2 p 2 exp( z/h) (z/h) 1/ z/h wind, 2 spec

18 particle velocity v x (z,l,h) p 2gh/4 hop-length/flight-time ~ free-fall/const.- approx v x z h l h/l ~ constant x

19 horizontal sand flux " z j h(z) = Z dhv x (h) P h(z,h) =q e z/ h h vertical sand flux `! `(z) = Z v z (z,h) = p 2g(h z) dhv z (z,h) P h(z,h) l(h)>` `(z = 0) = q erfcp` / h h/

20 horizontal sand flux field Z 50 " z 1 tunnel tunnel j h(z) = dhv x (h) P h(z,h) =q e z/ h h z [cm] vertical sand flux `! `(z) = Z v z (z,h) = p 2g(h z) dhv z (z,h) P h(z,h) l(h)>` `(z = 0) = q erfcp` / h h/

21 grain-scale experiments Rasmussen, Mikkelsen, Sedimentology (1998) Namikas, Sedimentology (2003) Rasmussen, Sørensen, J. Geophys. Res. (2008) Ho, Valance, Dupont, Moctar, Aeolian Research (2014) Durand, Claudin, Andreotti, PNAS (2014)

22 horizontal sand flux q rep e z/h hrep Two-species rep + approach qsal e z/h sal h sal j sal (z)+j rep (z) saltation reptation z/h sal

23 vertical sand flux 10 5 (0) + rep (0) sal /l sal

24 hop length distribution P (l z) / P [z,h(l)]@ l h(l) / e l/ h l Direct numerical simulations of aeolian sand ripples Orencio Durán a,b,1, Philippe Claudin a, and Bruno Andreotti a a Laboratoire de Physique et Mécanique des Milieux Hetérogènes, UMR 7636, CNRS, Ecole Supérieure de Physique et de Chimie Industrielles, Université Paris Diderot, Université Pierre et Marie Curie, Paris, France; and b MARUM Center for Marine Environmental Sciences, University of Bremen, D Bremen, Germany Edited by Harry L. Swinney, The University of Texas at Austin, Austin, TX, and approved September 17, 2014 (received for review July 10, 2014) -1.2 Aeolian sand beds exhibit regular patterns of ripples resulting from the interaction between topography and sediment transport. Their characteristics have been so far related to reptation transport caused by the impacts on the ground of grains entrained presented in ref. 26, we explicitly implement a two-way coupling between a discrete element method for the particles and a continuum Reynolds averaged description of hydrodynamics, coarse-grained at a scale larger than the grain size. This coupling occurs by means of drag and Archimedes forces in the equations of

25 particle velocity v x (z) =j(z)/ (z) r 4z v x (z) 1.5 ln 4 h/z h v z/h

26 particle velocity 6 (a) 4 (b) v(z) [m/s] (c) 15 (d) v(z) [m/s] gz/v 2 Œ 2gz/v 2 Œ

27 Summary analytical mesoscale model of aeolian transport based on grain scale physics ensemble of trajectories & two-species height-resolved observables applications to turbulent closure & data analysis & various mesoscale phenomena thank you! z h x l h/l